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A space elevator is an interesting concept, allowing for very low cost transit to orbit. Currently we don't seem to have a technology that will provide a strong enough cable to make the climb from Earth to Orbit.

Do we have the technology to build a space elevator anyplace in the solar system? If so where?

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Nowhere that would make sense and comes with the promised "free lunch" of such a construct. The biggest problem, on top of what you already suggested, is instability of equatorial orbits due to gravity anomalies. This works as a concept on a paper napkin scribble, in reality though, no celestial that we know of is free of gravitational anomalies. And once you start correcting for that, and constantly, that "free lunch" comes at a steep price that includes this space elevator's total rest mass in the equation.

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